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This work is an attempt to answer the question: How to use convex programming in shakedown analysis of structures made of materials with temperature-dependent properties. Based on recently established shakedown theorems and formulations, a dual relationship between upper and lower bounds of the shakedown limit load is found, an algorithmfor shakedown analysis is proposed. While the original problem is neither convex nor concave, the algorithm presented here has the advantage of employing convex programming tools.
An optimization method is developed to describe the mechanical behaviour of the human cancellous bone. The method is based on a mixture theory. A careful observation of the behaviour of the bone material leads to the hypothesis that the bone density is controlled by the principal stress trajectories (Wolff’s law). The basic idea of the developed method is the coupling of a scalar value via an eigenvalue problem to the principal stress trajectories. On the one hand this theory will permit a prediction of the reaction of the biological bone structure after the implantation of a prosthesis, on the other hand it may be useful in engineering optimization problems. An analytical example shows its efficiency.
Recently, in his vision for space exploration, US president Bush announced to extend human presence across the solar system, starting with a human return to the Moon as early as 2015 in preparation for human exploration of Mars and other destinations. In Europe, an exploration program, termed AURORA, was established by ESA in 2001 – funded on a voluntary basis by ESA member states – with a clear focus on Mars and the ultimate goal of landing humans on Mars around 2030 in international cooperation. In 2003, a Human Spaceflight Vision Group was appointed by ESA with the task to develop a vision for the role of human spaceflight during the next quarter of the century. The resulting vision focused on a European-led lunar exploration initiative as part of a multi-decade, international effort to strengthen European identity and economy. After a review of the situation in Europe concerning space exploration, the paper outlines an approach for a consistent positioning of exploration within the existing European space programs, identifies destinations, and develops corresponding scenarios for an integrated strategy, starting with robotic missions to the Moon, Mars, and near-Earth asteroids. The interests of the European planetary in-situ science community, which recently met at DLR Cologne, are considered. Potential robotic lunar missions comprise polar landings to search for frozen volatiles and a sample return. For Mars, the implementation of a modest robotic landing mission in 2009 to demonstrate the capability for landing and prepare more ambitious and complex missions is discussed. For near-Earth asteroid exploration, a low-cost in-situ technology demonstration mission could yield important results. All proposed scenarios offer excellent science and could therefore create synergies between ESA’s mandatory and optional programs in the area of planetary science and exploration. The paper intents to stimulate the European discussion on space exploration and reflects the personal view of the authors.
Cement augmentation is an emerging surgical procedure in which bone cement is used to infiltrate and reinforce osteoporotic vertebrae. Although this infiltration procedure has been widely applied, it is performed empirically and little is known about the flow characteristics of cement during the injection process. We present a theoretical and experimental approach to investigate the intertrabecular bone permeability during the infiltration procedure. The cement permeability was considered to be dependent on time, bone porosity, and cement viscosity in our analysis. In order to determine the time-dependent permeability, ten cancellous bone cores were harvested from osteoporotic vertebrae, infiltrated with acrylic cement at a constant flow rate, and the pressure drop across the cores during the infiltration was measured. The viscosity dependence of the permeability was determined based on published experimental data. The theoretical model for the permeability as a function of bone porosity and time was then fit to the testing data. Our findings suggest that the intertrabecular bone permeability depends strongly on time. For instance, the initial permeability (60.89 mm4/N.s) reduced to approximately 63% of its original value within 18 seconds. This study is the first to analyze cement flow through osteoporotic bone. The theoretical and experimental models provided in this paper are generic. Thus, they can be used to systematically study and optimize the infiltration process for clinical practice.